The present invention relates to a structure evaluation method used in the management of a manufacturing process of semiconductor device elements, a method for manufacturing a semiconductor device, and a recording medium.
In recent years, a process of forming a thin film such as an oxide film, a nitride film, or a polysilicon film, on a substrate is often used in manufacturing semiconductor devices. In order to produce a device using these thin films as elements and obtain desirable characteristics, the thickness and the physical properties of each thin film need to fall within predetermined ranges, respectively. Typically, the physical properties and the thickness of a thin film vary depending on the conditions of the process of forming the thin film (hereinafter xe2x80x9cthin film processxe2x80x9d) and the time period for which the process is performed. Therefore, after a thin film process is performed, it is evaluated as to whether the formed thin film has the predetermined thickness and physical properties. In the mass production of the device, it is necessary to change the process conditions when it is found from the evaluation results that the formed thin film does not have the desirable thickness and physical properties.
In a conventional thin film process, a thin film formed in a single process is basically a substantially homogeneous film whose composition and other physical properties do not substantially vary in the depth direction. On the other hand, it is often the case that a polysilicon film to be a gate electrode is deposited on a silicon oxide film to be a gate insulating film, as in the case of the gate section of an Si-MOS transistor. In most of such cases, the composition is substantially uniform within each layer with a well-defined interface between layers.
An optical evaluation method is a technique for evaluating the thickness and composition of a single-layer film or each layer of a multi-layer film on the substrate. As examples of the optical evaluation method, a spectroscopic ellipsometry method and a spectroscopic reflectance measuring method are widely used.
The spectroscopic reflectance measuring method is an evaluation method in which a sample is irradiated with light so as to obtain, for each of the separated wavelength regions, the ratio (reflectance) between the intensity of light that is used for irradiating the sample and the intensity of light that is reflected from the sample.
The spectroscopic ellipsometry method is an evaluation technique in which a sample is irradiated with linearly-polarized light so as to obtain information on the sample from the change in the polarization of the reflected light. Where a component of the linearly-polarized light whose electric field vector is parallel to the incident plane is denoted as a p-polarization component, another component whose electric field vector is perpendicular to the incident plane is denoted as an s-polarization component, and their complex reflectances are denoted by Rp and Rs, respectively, xcfx81xe2x89xa1Rp/Rs is also a complex number. Therefore, xcfx81 can be expressed as xcfx81xe2x89xa1tan xcexa8 ei xcex94 using two real numbers xcexa8 and xcex94. The spectroscopic ellipsometry method is used to measure the two physical amounts xcexa8 and xcex94 for each wavelength of light so as to obtain a spectrum.
A common nature of these optical evaluation methods is that since the phase and/or reflectance of light vary depending on the combination of the optical constants (refractive index n, extinction coefficient k) of the substance through which light passes, the measurement results include information on the optical constants of the substance. Moreover, since the light interference effects are significantly expressed in the optical information taken from the measurement object, the measurement results are often varied substantially by the thickness of the thin film, etc., whereby it is possible to obtain information on the thickness of the thin film, etc., with any of these evaluation methods.
However, the physical amount measured by the reflectance measuring method or the spectroscopic ellipsometry method (the reflectance in the case of the reflectance measuring method, and xcexa8 and xcex94 in the case of the spectroscopic ellipsometry method) includes the influences of all substances that are present in the path of light, and those influences cannot directly be extracted as separated information.
Therefore, when the spectroscopic reflectance measuring method or the spectroscopic ellipsometry method is used to measure a sample so as to evaluate the thickness and physical properties of a thin film, it is necessary to go through a procedure of comparing the actual measurement value with the estimated value of the measurement value, as follows.
FIG. 10 is a flow chart illustrating a management procedure for a conventional sample evaluation and thin film manufacturing process.
First, in step ST201, a sample A that has been produced by a process P is measured by an evaluation method M so as to obtain actual measurement values of a physical amount (e.g., xcex94, xcexa8).
On the other hand, a geometric model of the sample structure is set in step ST202, and an initial estimated value that defines the sample structure is set in step ST203, after which a theoretical estimated value of a physical amount measurement value is calculated in step ST204. Thus, in a case where an optical evaluation is used, the structure of a measurement sample (n and k profiles) is assumed, and the theoretical estimated value of the physical amount measurement value, which would be obtained if the n and k profiles were evaluated with the evaluation method M, is calculated.
Then, in step ST205, the actual measurement value of the physical amount and the theoretical estimated value are compared with each other. In this step, an evaluation value for evaluating the degree of difference between the actual measurement value and the theoretical estimated value is defined.
Then, in step ST206, it is determined whether the evaluation value is a local minimum value. If the evaluation value is not a local minimum, a new estimated value is set in step ST207, and then the process returns to the operation of step ST204 to repeat the operations of steps ST204 to ST206.
Then, if it is determined in the determination of step ST206 that the evaluation value is a local minimum, the process proceeds to step ST208 to decide on the estimated value of the sample structure, after which it is determined whether the sample structure is within an appropriate range in step ST209. If it is determined as a result of the determination that the sample structure is within the appropriate range, the process proceeds to step ST210 to perform the next operation with the process conditions that have been set.
On the other hand, if it is determined as a result of the determination in step ST209 that the sample structure is not within the appropriate range, the process proceeds to step ST211 to determine whether the geometric model of the sample structure is appropriate. If the geometric model of the sample structure is appropriate, the process proceeds to step ST212 to estimate the cause of the abnormal structure so as to take countermeasures such as changing the temperature, the time, the gas flow rate, etc.
If it is determined as a result of the determination in step ST211 that the geometric model of the sample structure is not appropriate, the process proceeds to ST213 to set a new geometric model, after which the process returns to step ST203 to repeat the operations of step ST203 and the subsequent steps.
As the evaluation value used in step ST205, a function which is normally a positive real number, which decreases as the difference between the actual measurement value and the theoretical estimated value decreases, and which becomes 0 when they are completely equal to each other, is used. Generally, it is often the case that a variance value "sgr" expressed by Expression (1) below:
"sgr"=xcexa3{aj(Sjxe2x88x92Smodj)2}xe2x80x83xe2x80x83(1) 
Which is obtained by adding together the squares of the differences between the actual measurement value and the theoretical estimated value for all wavelengths, is used as the evaluation value. Herein, Sj is the actual measurement value of the physical amount, and Smodj is the theoretical estimated value of the physical amount. Moreover, aj is a weighting coefficient, and information for various wavelengths are equally used for evaluation when all the weighting coefficients aj are 1. However, there are cases where the value of the weighting coefficient aj is set to other than 1 so that a wavelength at which the feature of the sample structure is likely to appear has a greater contribution.
With the least square method, an assumed sample structure for which the evaluation value is minimized is used as the measurement value. Thus, a sample structure (n and k profiles in the depth direction) that gives the same values xcexa8 and xcex94 as those of the actual measurement is sought for, and the sample structure that gives the closest values xcexa8 and xcex94 is used as the measurement value. However, with the spectroscopic ellipsometry method, the xcexa8 and xcex94 measurement results are varied by slight variations in the sample, e.g., variations in the optical constants on the surface atomic layer level. Thus, it is not possible to calculate the theoretical estimated value for every possible sample structure and compare it with the actual measurement value.
Therefore, in an actual evaluation, the sample structure is expressed by a small number of parameters so as to obtain, within an assumed range of values, the combination of parameter values for which the evaluation value is a local minimum. Moreover, while the evaluation value is a function of these parameters, the function is typically complicated, and it is practically very difficult to obtain the minimum value. In view of this, a local minimum value is used instead of a minimum value. A local minimum value can be obtained by algorithms such as a simulated annealing. With these algorithms, an arbitrary initial value is given to a parameter, and a slight variation is given to the parameter value in a direction such that the evaluation value decreases, so as to obtain a point where any slight variation would increase the evaluation value, i.e., the local minimum point. However, in the case of the method using the local minimum point, the obtained local minimum point may not be the point that gives the minimum value.
With a layered structure of single-composition films with well-defined interfaces, which is formed by a conventional thin film process, the thin film can be evaluated with a relatively good reproducibility with the method described above. This is because the structure that can be formed by such a process is simple, whereby the thin film structure can be expressed by a relatively small number of parameters, and because a local minimum point of the evaluation value is unlikely to occur, other than that for the combination of parameter values that gives a thin film model structure closest to the actual thin film structure.
Next, application of the conventional optical evaluation method described above to the evaluation of the thickness or characteristics of a crystal film containing a plurality of elements will be discussed.
In recent years, the epitaxial growth technique for crystal layers, which is by nature different from the conventional thin film process, has been used primarily for the production of an HBT (heterojunction bipolar transistor), or the like. The epitaxial growth technique is a technique of growing, on a crystal serving as an underlying base, such as a substrate, a new crystal having a structure that is in conformity with the structure of the atoms forming the underlying crystal. With this technique, the thickness can be controlled with a very high precision (typically about 1 nm, and even a single-atom layer under special conditions). Moreover, when the crystal to be grown is made of a material, such as SiGe, that forms a mixed crystal over a wide composition percentage range, it is possible to control the composition percentage. Therefore, utilizing these characteristics, it is possible to realize a state in which the composition varies approximately continuously in the depth direction with any profile. An example of a device utilizing this characteristic is a composition-graded SiGe-HBT. In the case of a composition-graded SiGe-HBT, the Ge composition is 0 in the emitter region and the Ge composition is gradually increased in the base region. As the Ge composition percentage increases, the band gap is narrowed, thereby generating an electric field in a direction of accelerating the carrier therein. As a result, the base transit time of the carrier is shortened, enabling a high speed operation of the transistor.
In such an SiGe composition-graded HBT, the composition is sometimes kept varying in the base region so as to provide a triangular profile. Typically, however, it is often the case that a trapezoidal profile with the addition of a buffer layer having a uniform Ge composition percentage is employed.
FIG. 11(a) is a diagram illustrating a Ge composition percentage profile in the depth direction of a layered structure that is formed by depositing an SiGe composition-graded layer and an Si cap layer on an SiGe buffer layer having a uniform composition.
As described above, those in the art have started to produce a structure whose composition varies approximately continuously by using the epitaxial growth technique. Accordingly, there has been a need for a method for evaluating a profile that varies approximately continuously while making a correction when the profile is deviated from a predetermined range.
In view of this, attempts have been made to evaluate a sample whose composition varies approximately continuously in the depth direction by using the spectroscopic ellipsometry method. In the evaluation process with the spectroscopic ellipsometry method, it is possible to measure xcexa8 and xcex94 with a sample having any composition profile. Moreover, it is possible to calculate the theoretical estimated values of xcexa8 and xcex94 by approximating a composition profile that varies approximately continuously to a sufficiently thin layered film.
Problems to be Solved
However, there have been problems as follows in forming a mixed crystal including a plurality of elements, such as an SiGe film, through epitaxial growth.
For an SiGe epitaxial growth film in which the Ge composition percentage can be varied on the atomic layer level toward the depth direction, unlike a thin film having a uniform composition, the number of sample structures that can possibly be taken increases significantly. Nevertheless, as long as the process conditions, that have been set, are accurately realized, the resulting thin film structure should substantially coincide with the intended thin film structure.
However, it was found when a crystal was grown intending to produce a thin film having a trapezoidal composition-graded profile, as illustrated in FIG. 11(a), for example, that the resulting thin film does not have an accurately trapezoidal composition profile if the crystal is grown at a temperature different from the set temperature.
It is believed that this is because the crystal growth rate depends on the substrate temperature and the dependence varies with the Ge composition percentage. If the Ge composition percentage in an SiGe crystal being grown increases during the growth of an SiGe film, the activation energy in the crystal growth decreases, whereby the change in the growth rate with respect to the change in the substrate temperature becomes small with respect to Si. As a result, if a crystal is grown under conditions such that the Ge composition percentage has a trapezoidal profile at a reference temperature, the Ge composition percentage of a composition-graded SiGe crystal that has been grown at a temperature higher than the reference temperature has a downwardly protruding profile, while the Ge composition percentage of a composition-graded SiGe crystal that has been grown at a temperature lower than the reference temperature has an upwardly protruding profile.
FIG. 11(b) is a diagram illustrating a Ge composition percentage profile in the depth direction of a layered structure having a composition-graded SiGe film grown at a temperature higher than the reference temperature.
FIG. 11(c) is a diagram illustrating a Ge composition percentage profile of a layered film having a Ge composition percentage profile as illustrated in FIG. 11(b), but with trapezoidal approximation. Specifically, when the structure of a layered film having a Ge composition percentage profile as illustrated in FIG. 11(b) is fit to a trapezoidal model employing the thickness of each layer and the Ge composition percentage as parameters, by using the spectroscopic ellipsometry method, a curve portion of the actual profile cannot be expressed, thereby obtaining, as the estimated value, a structure where the total thickness is substantially equal to the actual profile but the shape of an inclined portion is different from the actual shape. As a result, it is determined that the thicknesses of the Si cap and the SiGe buffer layer are thinner than they actually are, while determining that the thickness of the SiGe composition-graded layer is much thicker than it actually is, whereby it is erroneously determined that the growth time is longer than it actually is.
There is no geometric model that conveniently describes a Ge composition percentage profile as illustrated in FIG. 11(b). Therefore, in a conventional method for correcting the process conditions, a method of simply correcting the growth time of each layer of the layered film is used.
FIG. 11(d) is a diagram illustrating a Ge composition percentage profile in the depth direction of a layered film that is formed by correcting the thickness of each layer of the layered film by shortening the growth time based on the results of a trapezoidal approximation. As illustrated in the figure, when the process conditions are corrected by using, as the estimated value, the profile of the layered film obtained by the trapezoidal approximation as illustrated in FIG. 11(c), it is determined that the SiGe composition-graded layer is evaluated to be thicker than it actually is and thus this is corrected, thereby forming a layered film having an SiGe composition-graded layer that is thinner than the design value.
Thus, with the correction method used in the prior art, the Ge profile cannot be expressed appropriately with a geometric model, and thus cannot be evaluated correctly, thereby making an erroneous correction.
As described above, it is only a film that is grown at the reference temperature whose Ge composition percentage profile structure can be expressed by a trapezoid that is defined by the four parameters, i.e., the thicknesses of the Si cap layer, the composition-graded layer and the SiGe buffer layer, and the Ge composition percentage of the layers, as illustrated in FIG. 11(a). Therefore, even if the growth conditions are corrected based on the actual measurement value of the thickness of the grown SiGe film, etc., it is difficult to make an accurate correction as long as it is made on the assumption that the Ge composition percentage profile is always trapezoidal.
In view of this, the Ge composition percentage profile can be expressed at any temperature by increasing the number of parameters defining the Ge composition percentage profile of the film and expressing the Ge composition percentage profile with a polygon having more apexes than a trapezoid. However, when the number of parameters defining the Ge composition percentage profile is increased, the number of combinations of parameters that give a local minimum value of the variance value x described above increases significantly, whereby it is difficult to obtain a correct estimated value with a practical amount of calculation. Theoretically, if the number of parameters defining a geometric model structure such as a Ge composition percentage profile is increased, it is of course possible to express a sample structure closer to the actual structure. However, when the number of parameters is increased, there may be more than one combinations of parameter values that give a local minimum value of the evaluation value. As a result, the measurement results may be varied significantly for substantially the same sample structures by subtle variations in the xcexa8 and xcex94 measurements due to noise introduced in a measurement using the spectroscopic ellipsometry method, or a subtle difference in the sample structures such as a structure that is not included in the structure model, e.g., composition fluctuations at an interface.
An object of the present invention is to provide a structure evaluation method, a method for manufacturing a semiconductor device, and a recording medium, for grasping a process condition from a measurement value of a sample via a sample structure and correcting the process condition using the results so as to obtain a structure that is substantially as designed.
A structure evaluation method of the present invention includes the steps of: (a) obtaining a plurality of actual measurement values of a physical amount of an element of a semiconductor device by an optical evaluation method; (b) assuming a process condition for forming the element, and obtaining through calculation a structure of the element that is formed through a process using the assumed process condition; (c) calculating estimated values of a plurality of measurement values of a physical amount that are obtained when evaluating the structure of the element, which has been obtained in the step (b), by the optical evaluation method; and (d) estimating the structure of the element based on the plurality of actual measurement values of the physical amount of the element and the estimated values of the plurality of measurement values.
With this method, the most probable structure of the element is estimated in the step (d) based on the estimated value of the measurement value of the physical amount of the element based on the structure of the element that can actually be taken, which is obtained in the step (b), and the actual measurement value of the physical amount. Thus, unlike the conventional structure evaluation, which assumes a uniform structure, it is possible to perform an accurate structure evaluation that reflects the structure of the physical amount that varies as the process condition varies.
A numerical value for evaluating a difference between the plurality of actual measurement values of the physical amount and the estimated values of the plurality of measurement values is calculated in the step (d), so that the structure of the element is estimated through the steps (b) and (c) until the value is less than or equal to a threshold value. In this way, the structure evaluation can be facilitated by utilizing an algorithm such as a simulated annealing that utilizes the least square method, for example.
In the step (b), the calculation is performed by using a process simulator. In this way, it is possible to perform a structure evaluation conveniently and quickly.
Elements are formed in advance by processes using a plurality of process conditions and structures of the elements are obtained by the optical evaluation method so as to create a database of correlations between the plurality of process conditions and the structures of the elements formed by the process conditions; and in the step (b), the structure of the element is obtained through calculation based on the correlations. In this way, it is possible to perform a structure evaluation conveniently and quickly.
Significant effects can be provided by using the structure evaluation method of the present invention in a case where the process is an epitaxial growth process of a crystal film, and particularly in a case where the crystal film is a crystal film containing a plurality of elements.
In a case where the crystal film is a crystal film including a structure which contains Si and Ge and whose band gap varies in a graded manner, it is possible to perform a structure evaluation that can be used for controlling the Ge composition percentage profile. Specifically, even if the Ge composition percentage profile does not take a graded structure as designed due to the crystal growth rate being varied according to the Ge composition percentage, a Ge composition percentage profile that can actually occur is calculated as an estimated value of the measurement value of the physical amount, whereby it is possible to obtain an accurate Ge composition percentage profile in a crystal film for which actual measurement values have been obtained, by utilizing the estimated value of the measurement value of the physical amount.
It is preferred that the optical evaluation method is either a spectroscopic ellipsometry method or a spectroscopic reflectance measuring method.
A method for manufacturing a semiconductor device of the present invention includes the steps of: (a) obtaining a plurality of actual measurement values of a physical amount of an element of a semiconductor device by an optical evaluation method for one evaluation wafer of a plurality of wafers each including the element; (b) assuming a process condition for forming the element of the evaluation wafer, and obtaining through calculation a structure of the element that is formed through a process using the assumed process condition; (c) calculating estimated values of a plurality of measurement values of a physical amount that are obtained when evaluating the structure of the element, which has been obtained in the step (b), by the optical evaluation method; (d) estimating the structure of the element based on the plurality of actual measurement values of the physical amount of the element of the evaluation wafer and the estimated values of the plurality of measurement values; and (e) determining whether or not to correct the process condition of the process at least for wafers of the plurality of wafers other than the evaluation wafer based on a difference between the estimated structure of the element of the evaluation wafer and a designed structure of the plurality of wafers.
With this method, it is possible to change/set the process condition for the other wafers after accurately grasping the structure of the element of the evaluation wafer by using the structure evaluation method described above, whereby it is possible to improve the characteristics of a semiconductor device and to reduce the variations in the characteristics thereof.
Significant effects can be provided by using the method for manufacturing a semiconductor device of the present invention in a case where the process is an epitaxial growth process of a crystal film, and particularly in a case where the crystal film is a crystal film containing a plurality of elements.
In a case where the crystal film is a crystal film including a structure which contains Si and Ge and whose band gap varies in a graded manner, it is possible to accurately control the Ge composition percentage profile. Specifically, even if the Ge composition percentage profile does not take a graded structure as designed due to the crystal growth rate being varied according to the Ge composition percentage, a Ge composition percentage profile that can actually occur is calculated as an estimated value of the measurement value of the physical amount, whereby it is possible to obtain an accurate Ge composition percentage profile in a crystal film for which actual measurement values have been obtained, by utilizing the estimated value of the measurement value of the physical amount.
A recording medium of the present invention is a recording medium that can be taken into a computer used for performing a characteristic evaluation of an element of a semiconductor device by an optical evaluation method, the recording medium being a computer-readable recording medium storing therein a program for instructing the computer to execute the procedures of: (a) taking a plurality of actual measurement values of a physical amount of the element of the semiconductor device; (b) assuming a process condition for forming the element, and obtaining through calculation a structure of the element that is formed through a process using the assumed process condition; (c) calculating estimated values of a plurality of measurement values of a physical amount that are obtained when evaluating the structure of the element, which has been obtained in the procedure (b), by the optical evaluation method; and (d) estimating the structure of the element based on the plurality of actual measurement values of the physical amount of the element and the estimated values of the plurality of measurement values.
In this way, it is possible to automatically perform the structure evaluation by using a computer.
It is preferred that a numerical value for evaluating a difference between the plurality of actual measurement values of the physical amount and the estimated values of the plurality of measurement values is calculated in the procedure (d), so that the structure of the element is estimated through the procedures (b) and (c) until the value is less than or equal to a threshold value.